We study TE-wave propagation in a hollow waveguide with a graded transition from a lossy right-handed material (RHM) filling the left-hand half of the waveguide to the impedance-matched lossy left-handed material (LHM) filling the right-hand half of the waveguide. The transition between the two media is graded along the direction perpendicular to the boundary between the two materials (chosen to be the z-direction), and the permittivity epsilon(omega, z) and permeability mu(omega, z) are chosen to vary according to hyperbolic tangent functions along the z-direction. We obtain exact analytical solutions to Maxwell's equations for lossy media, and the solutions for the field components confirm the expected properties of RHM-LHM structures. Thereafter, a numerical study of the wave propagation over an impedance-matched graded RHM-LHM interface is performed, using COMSOL software. The numerical study shows an excellent agreement between the numerical simulations and analytical results. Compared to other solution methods, the present approach has the advantage of being able to model more realistic smooth transitions between different materials. However, in the limiting case, it includes correct results for abrupt transitions as well. In the present approach we also introduce interface width as an additional degree of freedom that can be used in the design of practical RHM-LHM interfaces.

In this paper, we study TEM-wave propagation inside a hollow coaxial waveguide filled with an inhomogeneous metamaterial composite, with a graded transition between a right-handed material (RHM) and an impedance-matched left-handed material (LHM). The graded transition and the TEM-wave propagation occur in the direction perpendicular to the boundary between the two media, which has been chosen to be the z-direction. The relative permittivity epsilon(omega, z) and permeability mu(omega, z) of the RHM-LHM composite vary according to hyperbolic tangent functions along the z-direction. The exact analytical solutions to Maxwell's equations are derived, and the solutions for the field components and wave behavior confirm the expected properties of impedance-matched RHM-LHM structures. Furthermore, a numerical study of the wave propagation over an impedance-matched graded RHM-LHM interface, using the COMSOL Multiphysics software, is performed. An excellent agreement between the analytical results and numerical simulations is obtained, with a relative error of less than 0.1%. The present method has the ability to model smooth realistic material transitions, and includes the abrupt transition as a limiting case. Finally, the RHM-LHM interface width is included as a parameter in the analytical and numerical solutions, allowing for an additional degree of freedom in the design of practical devices using RHM-LHM composites. Published by Optica Publishing Group under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

We study TEM-wave propagation inside a hollow coaxial waveguide filled with a periodic composite of lossy impedance-matched right-handed (RHM) and left-handed (LHM) media. The z-direction, chosen as the direction perpendicular to the boundaries between the two media, is where the transitions and TEM-wave propagation take place. The relative permittivity epsilon(omega, z) and permeability mu(omega, z) of the periodic RHM-LHM composite vary according to an arbitrary periodic function f(z) along the z-direction. In particular, we consider two specific periodic permittivity and permeability profiles: one with abrupt RHM-LHM transitions and one with linear RHM-LHM transitions. The expected properties of impedance-matched periodic RHM-LHM structures are confirmed by the derived precise analytical solutions to Maxwell's equations, which also include solutions for the wave behavior and field components. Furthermore, a numerical study of the wave propagation over the impedance-matched graded RHM-LHM composites is performed using the COMSOL Multiphysics software. The resulting numerical simulations and analytical results were virtually identical. The present method can model smooth, realistic material transitions and includes the abrupt transition as a limiting case.

In this paper, we study transverse electric (TE) wave propagation inside a hollow circular waveguide filled with a lossy graded multilayered dielectric composite. The dielectric composite grading and the wave propagation are directed along the z-direction. The z-dependent permittivity of the dielectric composite is modeled using a periodic sinusoidal function. The exact analytical solutions to Maxwell's equations are obtained, and the field solutions and wave behavior confirm the expected properties of a lossy graded multilayered dielectric medium inside a hollow circular waveguide. Thereafter, through a numerical study performed using the commercial software COMSOL Multiphysics, we show that the analytical and numerical results are in perfect agreement. The analytical model applies to any combination of the material parameters relevant to the graded multilayered dielectric medium. The significance of the proposed method is that it can be utilized for analytically studying wave propagation and wave phenomena in a variety of media with characteristics including, but not limited to, periodicity, grading, negative refraction, and spatial- and frequency dependence. The validity is not restricted to any given frequency regime, therefore, allowing the proposed method to be useful for different types of applications, such as super-resolution imaging, electromagnetic cloaking, sub-wavelength focusing, and microwave absorbers.